Gauss–Seidel method for multi‐valued inclusions with Z mappings

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Article ID:	iaor20123830
Volume:	53
Issue:	1
Start Page Number:	97
End Page Number:	105
Publication Date:	May 2012
Journal:	Journal of Global Optimization
Authors:	Schaible S, Allevi E, Gnudi A, Konnov I
Keywords:	programming: nonlinear

Abstract:

We consider a problem of solution of a multi‐valued inclusion on a cone segment. In the case where the underlying mapping possesses Z type properties we suggest an extension of Gauss–Seidel algorithms from nonlinear equations. We prove convergence of a modified double iteration process under rather mild additional assumptions. Some results of numerical experiments are also presented.

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